Welcome to the website of the project "Axiomatizing Metatheory - Frege's New Science", an FWF-funded research project that aims to re-evaluate some of the lesser-known aspects of the so-called Frege-Hilbert controversy (Project number: P 30448). The project has a specific focus on a proposal made by Frege where he claims that a "new science" has to be devised in order to study metatheoretical questions such as the consistency and mutual independence of axioms. The main aims of the project are
- to make clear what Frege's New Science is supposed to look like exactly and how it relates to concepts and methods in modern and pre-modern mathematical logic.
- to clarify Frege's motivation for introducing a New Science in the first place, and what his proposal implies for his philosophy of logic and mathematics.
- to determine whether, and, if so, to what extent, Frege's conception of metatheoretical investigations might be reflected in contemporary discussions in the philosophy of logic.
- Frege and the Origins of Model Theory in Nineteenth Century Geometry, Synthese (2019), https://doi.org/10.1007/s11229-019-02421-4.
Abstract Full Text
- Truth, Paradox, and the Procedural Conception of Fregean Sense, Philosophy of Logic and Mathematics: Proceedings of the 41st International Wittgenstein Symposium, Berlin/Boston: DeGruyter, 153-168 (2019).
- Hilbert, Duality, and the Geometrical Roots of Model Theory (with Georg Schiemer), Review of Symbolic Logic, 11 (1), 48-86 (2018).
Abstract Full Text
- Projective Duality and the Rise of Modern Logic
- Frege on Objecthood and Intuition in Projective Geometry
- A Formal Reconstruction of (Blanchette's Reading of) Fregean Provability
- Meaning, Truth, and Paradox
- 07/2019, Do any two lines meet in a point? Frege on (projective) Geometry. 2nd Prague Workshop on Frege's Logic, Institute of Philosophy, AKC, Prague.
- 02/2019, Meaning, Truth, and Paradox. Annual Conference of the Israeli Philosophical Association, Bar-Ilan University, Ramat Gan.
- 03/2019, Frege and Semantics. FregeFest VI, UC Irvine.
- 08/2018, Truth, Paradox, and the Procedural Conception of Fregean Sense. 41st International Wittgenstein Symposium, Kirchberg.
- 05/2018, The Procedural Conception of Fregean Sense. Work-in-Progress Seminar of the Department of Philosophy (KGW), Salzburg.
- 02/2018, Frege, Hilbert, and the Origins of Model Theory in 19th Century Geometry. Workshop Modern Axiomatics and Early Metatheory, Vienna.
- December 6-7, 2018: "Axiomatizing Metatheory - Truth, Provability, and Beyond". Workshop.